4.1(BINOMIAL EXPANSION)

Question 1

What is pascals tringle?

Answer 1

. 1 0
1 1 1
1 2 1 2
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

0 1 2 3 4 5
^4C_2=6

Question 2

Explain ^n C_r

Answer 2

nth row of pascals triangle (remember it starts at 0)
rth position in the row
^n C_r= n!/(n-r)! x r!

Question 3

What is ! ?

Answer 3

Factorial.
4!= 1x2x3=6
0!=1

Question 4

How to find the result of a binomial expansion?

Answer 4

For a single result times the result of ^n C_r by a^(n-r) and by mx^(r)
e.g. (3+2x)^12, find the coefficient of x^5
^12 C_5 = 792
3^7= 2187
2x^5= 32x^5
792 x 2187 x 32x^5=554273238

For the whole result use the whole row with descending first terms finishing at ^0 and ascending first terms starting at ^0
e.g. (2-x)^5
1 5 10 10 5 1
32 16 8 4 2 1
(-x)^0 (-x)^1 (-x)^2 (-x)^3 (-x)^4 (-x)^5

32-80x + 80x^2 - 40x^3 +10x^4 - 5x^2